2009.04.10-ECE659-L34-notes

2009.04.10-ECE659-L34-notes - f = = u d F F = if we get 1 2...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 34: Second Law Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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H s Σ 2 Σ 1 Σ 2 μ 1 1 T 2 T ( 29( 29 1 2 q I dET E f f h = - For current flow: ( 29 ( 29 ( 29 1,2 1,2 1 2 1 Q I dET E E f f h = - - 1 2 Q Q W - = 1 2 1 2 Q Q T T < (first law) (second law) ( 29 ( 29 1 1 2 2 1 2 1 2 1 2 1 2 1 2 1 1 1 1 B B E k T E k T f f e e E E T T Q Q T T - - + + - - < <
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Anti-parallel spin valve device: H s Σ 2 Σ 1 Σ 1 γ 2 2 μ 1 I V All impurities in up direction: 2 1 No impurities: I V With spin flip impurities: If μ1 > μ2 (V is positive): If μ1 < μ2 (V is negative): 0 0 I I = I V
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( 29 ( 29 1 1 d u d u d u F f f I dE F f f - - - 1 2 , u d f f f
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Unformatted text preview: f = = u d F F = if we get 1 2 f f-At non-zero temperatures: ( 29 ( 29 ( 29 ( 29 ( 29 2 1 1 2 2 1 2 1 1 * 1 E kT E kT u d kT f f F e e F f f e μ-----= =-= ( 29 1 2 ln u oc d F kT F-= u d F F ≫ if we get 1 2 1 I V We get non-zero current for zero voltage 2 1 ( 29 ( 29 ( 29 1 1 * 1 B B E k T E k T f f E e f e---= = + 2...
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2009.04.10-ECE659-L34-notes - f = = u d F F = if we get 1 2...

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